There are hotkeys you can set for "load ships onto transports" and "special unload".
The load command makes everything you've currently selected hop into whatever transport they can, prioritizing nearby ones, but if there's enough space they'll find one somewhere. No more micro!
The special unload lets you unload SPECIFIC ships. Click once to unload one, ctrl for five, alt for all. Yay, now you can select your whole fleet and unload all the bombers! Or only the MkII+ to deal with an ion cannon. Or only one of your colony ships. Etc.
All of a sudden, transports are a joy instead of a pain, and using them to get things routinely from point A to point B feels much more natural.